1. Field of the Invention
The present invention generally relates to semiconductor chip manufacturing, and more particularly to a method for calibrating an optical proximity correction model used for printing a circuit pattern on a semiconductor wafer.
2. Description of the Related Art
Optical Proximity Correction (OPC) uses calibrated optical and resist models to modify the shapes on the mask so that the printed shapes on the wafer will closely match the desired target shapes, within acceptable criteria. OPC optical and resist models are developed through an empirical method using a model calibration process in which test structures (also called calibration structures), that are intended to be a representative set of the actual product patterns, are placed on a test mask. Thus, the calibration test patterns consist of features that have dimensions that are desired to be printed on the wafer. The test mask is then exposed and the wafer image is measured and used as input in the model calibration and building process.
Optical model calibration is performed using direct measurements of the printed test pattern exposed by the illumination source. Referring to FIG. 1A, energy 100 from the illumination source (not shown) illuminates a cross-section view of a portion of an dark field mask 200 that has a substantially opaque field region 210 and transparent region 205, representing a feature to be printed, through which the illumination energy is transmitted to the resist on a wafer substrate. The plot 300 schematically illustrates the intensity I of illumination energy for various exposure dose settings (Dose1, Dose2, Dose3) along the horizontal direction x. A resist image will be formed when the intensity I of the light equals or exceeds a threshold value 15 at which the resist will develop. As the energy dose, or equivalently, the intensity, increases (from Dose3 to Dose1), the extent of energy that exceeds the threshold increases, e.g. from Dose3 to Dose2 to Dose1, and the corresponding dimension printed on the wafer, i.e. CD3 to CD2 to CD1, respectively, of the pattern image formed on the wafer increases.
A constant threshold resist model assumes that the threshold for image development is constant across the wafer. However, in practice, the constant threshold model does not necessarily represent the actual behavior of the resist across the wafer. To account for such variations, a typical resist model uses is a “variable threshold resist model”. A variable threshold model uses a fitting polynomial to correct the deviation from the constant threshold and find the best value for each feature threshold that makes the predicted CDs of the pattern match as closely as possible the experimentally measured CDs of pattern features printed using the test mask.
A variable threshold model may be represented by Equation 1:Variable Threshold=Constant Threshold+Correction Polynomial  (1)
The variable threshold model comprises a constant threshold plus a correction polynomial, as in Equation 1. The independent variables in the correction polynomial are image parameters, such as Imin, Imax, slope, etc., as known in the art. The calibration process includes determining the values of the constant threshold and the coefficients of the correction polynomial. These are determined by finding, for all of the features in the test pattern, a best fit of measured CDs to the CDs predicted by the model. This calibration usually includes performing a simulation of the optical image produced by the test pattern. Then, referring to FIG. 1B, the maximum intensity (Imax) and the minimum intensity (Imin) are determined for each feature in the test pattern from the simulated optical image. Imax is the maximum intensity in the neighborhood of the simulated image of feature 205 on the mask 200, and similarly, Imin is the minimum intensity in the neighborhood of the simulated image of feature 205. The resulting values of Imax and Imin may be plotted as a function of pattern feature number, for example, as illustrated in FIG. 2A. It is generally expected that the Imax values are confined to a region 201 of the plot, while the Imin values are confined within a second region 202 of the plot that does not overlap with the intensities of the region 201 comprising the Imax values. The constant threshold should be identified within the gap region 203 between the region 201 consisting of Imax values, and bounded below by a minimum Imax intensity value, and the region 202 consisting of Imin values and bounded above by a maximum Imin value, for the entire test pattern. The gap region 203 has a finite width based on the range of feature sizes in prior art test patterns that reflect the dimensions of circuit features to be printed.
However, selecting a single, accurate constant threshold intensity value within the finite gap 203 is generally performed by trial and error, which may not provide a sufficiently accurate result. For example, FIG. 3 illustrates a comparison of overlays of simulated images to a scanning electron microscope (SEM) image 300 of a feature printed on the wafer. Each of the three simulated image contours 311, 312 and 313 are from a variable resist model, each having a different constant threshold value that was chosen within the gap between Imin and Imax in a plot similar to that of FIG. 2. The shortest contour image 311 results from using a constant threshold value of about 0.225, the middle contour image 312 resulted from using a larger constant threshold value of about 0.25, and the longest contour image 313 resulted from using an even larger constant threshold value of about 0.275. Each of these constant threshold values occur within the acceptable gap of a plot similar to FIG. 2 typically formed according to prior art calibration methods. It can be seen that the variable threshold model using the larger constant threshold value of 0.275 resulted in an image 313 that more closely matches the actual SEM image, and that merely choosing the constant threshold value can result in significant deviations in the predicted image contour. As can be seen, a slight variation in the constant threshold value may result in a very different prediction of the wafer image.
In view of the foregoing considerations, there is a need for a method to identify reliably an accurate constant threshold for a given process that can be used in a variable threshold resist model that may be used during the mask design process, for example, in OPC or mask verification methodologies.